-5t^2+60t+30=0

Solution for -5t^2+60t+30=0 equation:

Simplifying
-5t2 + 60t + 30 = 0

Reorder the terms:
30 + 60t + -5t2 = 0

Solving
30 + 60t + -5t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '5'.
5(6 + 12t + -1t2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(6 + 12t + -1t2)' equal to zero and attempt to solve:

Simplifying
6 + 12t + -1t2 = 0

Solving
6 + 12t + -1t2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-6 + -12t + t2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -12t + 6 + t2 = 0 + 6

Reorder the terms:
-6 + 6 + -12t + t2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -12t + t2 = 0 + 6
-12t + t2 = 0 + 6

Combine like terms: 0 + 6 = 6
-12t + t2 = 6

The t term is -12t.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12t + 36 + t2 = 6 + 36

Reorder the terms:
36 + -12t + t2 = 6 + 36

Combine like terms: 6 + 36 = 42
36 + -12t + t2 = 42

Factor a perfect square on the left side:
(t + -6)(t + -6) = 42

Calculate the square root of the right side: 6.480740698

Break this problem into two subproblems by setting 
(t + -6) equal to 6.480740698 and -6.480740698.

Subproblem 1
t + -6 = 6.480740698

Simplifying
t + -6 = 6.480740698

Reorder the terms:
-6 + t = 6.480740698

Solving
-6 + t = 6.480740698

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '6' to each side of the equation.
-6 + 6 + t = 6.480740698 + 6

Combine like terms: -6 + 6 = 0
0 + t = 6.480740698 + 6
t = 6.480740698 + 6

Combine like terms: 6.480740698 + 6 = 12.480740698
t = 12.480740698

Simplifying
t = 12.480740698

Subproblem 2
t + -6 = -6.480740698

Simplifying
t + -6 = -6.480740698

Reorder the terms:
-6 + t = -6.480740698

Solving
-6 + t = -6.480740698

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '6' to each side of the equation.
-6 + 6 + t = -6.480740698 + 6

Combine like terms: -6 + 6 = 0
0 + t = -6.480740698 + 6
t = -6.480740698 + 6

Combine like terms: -6.480740698 + 6 = -0.480740698
t = -0.480740698

Simplifying
t = -0.480740698

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {12.480740698, -0.480740698}
Solution
t = {12.480740698, -0.480740698}